This invention relates generally to methods and apparatus for optically determining physical parameters of thin films deposited on a complex substrate, and in particular to measurements of thin films on complex substrates for obtaining physical parameters such as thickness t, refraction index n and extinction coefficient k.
The determination of physical parameters of thin films is very important, since many modern technologies rely on thin films for various functions. For example, thin films are used for optical and/or mechanical protection of surfaces, alteration of surface optical and/or mechanical properties and for many other purposes. For example, in the manufacture of magnetic hard disks thin films exhibiting high hardness and high wearing resistance (e.g., diamond-like-carbon (DLC)) are used to protect the disk surface.
The most commonly investigated physical parameters of thin films include their thickness t, index of refraction n, extinction coefficient k, surface roughness "sgr" (at the interface between the thin film and the substrate on which it is deposited) and energy bandgap Eg which is related to extinction coefficient k. Knowledge of parameters t, n and k tends to be most important in practical applications. In particular, the thickness t of the thin film is frequently crucial and has to be known to a very high degree of accuracy. This presents considerable difficulty, since t for thin films typically ranges from 1,000 Angstroms down to tens of Angstroms and less. In this range, typical optical measurements are not very reliable.
Various prior art techniques exist for examining thin films. U.S. Pat. No. 3,601,492 to Reichert employs a standard interference technique for measuring film thickness based on observing the interference between the light reflected from the top and bottom surfaces of the thin film. Greenberg et al. teaches in U.S. Pat. No. 5,042,949 that film thickness can be determined by examining the interference pattern and reflectance data from a reflectance pattern, respectively to determine film thickness profile. In U.S. Pat. No. 4,999,509 Wada et al. describe a how to measure thicknesses of several films using a reflectance measuring device.
Still another approach to determining thin film thickness is taught by Hattori et al. in U.S. Pat. No. 5,371,596. In accordance with this technique the light from a light source is modulated to produce a modulated interference light. This modulated light is reflected from the thin film and used by a number of photodetectors to derive film thickness.
Ellipsometry is another technique used to measure physical parameters of thin films. In this method n and k are determined by measuring the change in the state of polarization of the reflected light. Ellipsometry requires complex instrumentation and needs certain sophistication in interpretation of the measurements.
Unfortunately, the above prior art approaches yield less and less satisfactory results for the thin film parameters with decreasing film thickness due to poor signal-to-noise ratios.
To overcome these limitations, several prior art techniques rely on comparisons of reflectance data obtained from thin films and monitoring samples. For example, Sandercock teaches in U.S. Pat. No. 4,355,903 to compare the reflection of polychromatic light from a reference or standard thin film with the reflection obtained from a film of unknown thickness. Mumola teaches in U.S. Pat. No. 5,337,150 the use of a separate reference wafer which has a thin film layer similar to that being coated on the actual wafer. A broadband beam of radiation illuminates the sample wafer and yields a reflected beam having a unique spectral radiation (spectral signature). Film thickness is identified when the spectral pattern of this reflected beam matches that of the beam reflected from the reference wafer. Similarly, U.S. Pat. No. 5,101,111 to Kondo teaches a method of measuring film thickness using a reflectance sample having a known reflectance for each value of film thickness dx. The reflectances for the various thicknesses are stored in a table and compared to those obtained when examining a sample.
In U.S. Pat. No. 4,555,767 Case et al. disclose a technique and apparatus for measuring the thickness of epitaxial layers by infrared reflectance. The technique relies on taking the Fourier transform of the signal reflected from the epi layer using a Fourier transform IR spectrometer and comparing the result with theoretical values obtained beforehand. In U.S. Pat. No. 5,523,840 Nishizawa et al. also rely on a Fourier transformation to obtain an interference waveform dispersion spectrum which is compared with a waveform obtained by numerical calculation using an optical characteristic matrix. Waveform fitting between theoretical and measured spectra is used to obtain film thickness. U.S. Pat. No. 5,241,366 to Bevis et al. discloses a thin film thickness monitor which performs the measurement based on a comparison between the reflection of polychromatic light from a reference thin film and the sample thin film. U.S. Pat. No. 5,365,340 to Clapis et al. and U.S. Pat. No. 5,555,472 to Ledger also teach how to measure film thicknesses based on reference samples yielding reference reflectance signals.
All of the above optical approaches to measuring thin film thickness and any other physical parameters of the thin film are complicated and not capable of providing the desired levels of accuracy. In particular, the above techniques can not be used for measuring thin films in thickness ranges of tens of Angstroms with an accuracy of less than 5 Angstroms. Moreover, none of these methods can determine the n, k and t values of a thin film simultaneously.
The prior art also teaches non-optical methods of determining thin film thicknesses. For example, atomic force microscopy (AFM) employing a deflectable stylus can be used to determine film thicknesses by surface profiling. The drawbacks of this technique are that it requires a physical step which is destructive to the thin film or degrades its surface. In addition, this technique can not be used to determine other physical parameters of the thin film, such as the n, k and Eg values.
In U.S. Pat. No. 4,905,170 Forouhi et al. describe an optical method for determining the physical parameters of a thin film in amorphous semiconductors and dielectrics. This technique is very accurate and it takes into account the quantum mechanical nature of the light and thin film interaction. Unfortunately, it can not generate sufficiently accurate thickness readings and simultaneously determine n and k values for thin films deposited on substrates having a relatively xe2x80x9csmoothxe2x80x9d reflectance spectrum. Such substrates are very commonly used, however, and include many typical substrate materials, e.g., Si, quartz, Mg, Cr and Ni and AlTiC alloys used in the semiconductor and magnetic storage technologies as well as polycarbonate (PC) used in optical disks.
Hence, there is a pressing need to develop an approach which will enable one to measure the thickness as well as other physical properties of thin films on various substrates to a high degree of accuracy. Specifically, it would be very desirable to provide a non-destructive measurement method for determining film thickness to an accuracy of 5 to 2 Angstroms or less in films whose thickness is less than 100 Angstroms or even less than 10 Angstroms. Furthermore, the method should be capable of identifying additional physical parameters of the thin film such as the values of n, k and Eg.
Accordingly, it is a primary object of the present invention to provide a method and an apparatus for optically determining physical parameters of thin films. In particular, the apparatus and method should enable one to determine film thickness t to within 5 Angstroms and yield accurate values of physical parameters including n, k and Eg.
It is another object of the invention to enable one to evaluate the above physical parameters of thin films in a non-destructive manner.
Yet another object of the invention is to provide for the apparatus of the invention to be simple and cost-effective to implement. Additionally, the method of the invention should be easy to employ in practical situations.
The above objects and advantages, as well as numerous improvements attained by the apparatus and method of the invention are pointed out below.
These objects and advantages are secured by a method for optically determining a physical parameter including thickness t, index of refraction n and extinction coefficient k of a thin film. The method can also be used to determine related physical parameters, such as energy bandgap Eg related to the extinction coefficient k of the material of the thin film. The method calls for providing a test beam having a wavelength range xcex94xcex and providing a complex substrate which has at least two layers and exhibits a non-monotonic and an appreciably variable substrate optical response over wavelength range xcex94xcex. The thin film is deposited on the complex substrate. A measurement of a total optical response, consisting of the substrate optical response and an optical response difference due to the thin film is performed over wavelength range xcex94xcex. The physical parameters are then determined from the total optical response.
In one case the substrate optical response is a substrate reflectance and the total optical response is a total reflectance due to the reflectance of the substrate and a reflectance difference due to the presence of the thin film. Thus, illumination with the test beam produces a reflected beam.
The reflected beam can be analyzed to determine the physical parameter from any one or from any combination of the properties of light making up the reflected beam. These properties include phase, amplitude, s-polarization, p-polarization, s-polarization amplitude, p-polarization amplitude, s-polarization phase and p-polarization phase. In a particular case, the reflectance measurement can involve an ellipsometric technique.
When the optical response examined is reflectance, the step of determining the physical parameters is based on a model of n and k of the substrate and thin film. In the preferred embodiment the Forouhi-Bloomer method is used for modeling n and k. Other dispersion models can also be used. In some cases, no dispersion model is necessary. The model yields a theoretical total reflectance value RT(th) and this theoretical value is compared to the total reflectance RT obtained during the measurement. The comparison of these values is performed and the parameters of the model are adjusted to conform with the observed value. The values of the physical parameters are then obtained from the model. The fitting of the theoretical and measured values can be performed by a fitting technique such as non-linear least squares fit, a mean absolute difference fit or any other suitable technique.
The physical parameters can also be determined based on optical transmittance. In this case the optical response is a substrate transmittance and the total optical response is a total transmittance due to the transmittance of the substrate and a transmittance difference due to the presence of the thin film.
Illumination with the test beam produces a transmitted beam. The transmitted beam can be analyzed to determine the physical parameter from any one or from any combination of the properties of light making up the transmitted beam. As in the case of the reflected beam, the properties of the transmitted beam which can be examined include phase, amplitude, s-polarization, p-polarization, s-polarization amplitude, p-polarization amplitude, s-polarization phase and p-polarization phase. In a particular case, the transmittance can be analyzed by an ellipsometric technique.
The step of determining the physical parameter from the transmitted beam can be based on transmittance model of the substrate and thin film. The model yields a theoretical total transmittance value TT(th) and this theoretical value is compared to the total transmittance TT obtained during the measurement. As in the reflective approach, the value of the physical parameters is obtained from the model. A fitting technique such as non-linear least squares fit, a mean absolute difference fit or any other suitable technique can be employed as well. In the preferred embodiment the Forouhi-Bloomer method is used for modeling transmittance. Other dispersion models can also be used. In some cases, no dispersion model is necessary.
The complex substrate is selected to have a non-zero, non-monotonic and appreciably variable substrate optical response over wavelength range xcex94xcex. This can be achieved when the at least two layers making up the complex substrate are chosen such that the effect of multiple internal reflections in the complex substrate and the film is maximized.
An apparatus for optically determining the physical parameters of the thin film employs the complex substrate which is made up of at least two layers and has the above-mentioned substrate optical response characteristics over wavelength range xcex94xcex. The apparatus has a light source for illuminating the complex substrate and the thin film deposited on it with a test beam spanning the wavelength range xcex94xcex. A detector is provided for measuring the total optical response, e.g., a reflected beam and/or a transmitted beam. A computing unit in communication with the detector determines the physical parameter from the total optical response.
The material composition of each of the layers is selected such that optical response difference is non-zero, non-monotonic and appreciably variable over xcex94xcex. For example, the materials are SiO2, Si or SiOxNy. These materials and their thicknesses are selected to maximize the effect of multiple internal reflections in the complex substrate and the thin film. The apparatus can be adapted for making measurements of transmittance and/or reflectance of the complex substrate and the thin film. The physical parameters are determined by the computing unit which obtains its data from the detector set up to detect the transmitted or reflected beam.
A polarizer can be provided to polarize the test beam. Another polarizer, or analyzer, can be placed in the path of the reflected or transmitted beam. The use of such polarizers or analyzers depends on what kind of light characteristics, i.e., s-polarization or p-polarization or their ratios (ellipsometric techniques), of the reflected or transmitted beams are measured to determine the physical parameters of the thin film.
Furthermore, a monitoring sample for optically monitoring the physical parameter of a thin film in accordance with the invention can be used in a monitoring system. For example, a deposition chamber for depositing thin films on a substrate can employ a monitoring sample to determine from it the physical parameters of the thin film being deposited on the substrate. Of course, the monitoring sample can be measured in the reflective or transmissive arrangement, as necessary or preferable.
In another embodiment of the invention, the thin film whose physical parameters are to be determined can be deposited between two of the layers making up the complex substrate. In this case the complex substrate is likewise designed to maximize the effect of multiple internal reflections within the substrate and the thin film.
The particulars of the invention and its various embodiments are described in detail in the detailed description section with reference to the attached drawing figures.